2nd evolution requires a total of 5 mats: 2 Birds matching the unit type (slice/hit/pierce/magic), 2 Petals matching the unit's nationality and an elixir matching the unit's rarity.
Birds can be purchased with Sun Crystals @330 each.
Petals can be purchased with Life Crystals @150 each (they can supposedly drop elsewhere but I haven't seen that happen yet).
Elixirs need to be farmed from the Special Mission.